JEE 2022 — Mathematics PYQ

Solution

1. Simplify the second part of the expression:

• The expression $(p\vee q)\Rightarrow q$ is equivalent to $\sim (p\vee q)\vee q$.

• Using De Morgan's Law: $(\sim p\wedge \sim q)\vee q\equiv (\sim p\vee q)\wedge (\sim q\vee q)\equiv (\sim p\vee q)\wedge T\equiv (\sim p\vee q)$.

• This is further equivalent to $p\Rightarrow q$.

2. Test the options for $(p\wedge q)\Delta (p\Rightarrow q)$:

• If $\Delta$ is $\Rightarrow$: $(p\wedge q)\Rightarrow (p\Rightarrow q)$.

• Since $p\wedge q$ implies both $p$ and $q$, and $q$ alone implies $p\Rightarrow q$ (as $T\Rightarrow T$ is $T$), the entire implication is a tautology.

Correct Option: (C)